Atozuke 「後付け」 is the state of a "yakuless" tenpai hand, that gains yaku upon the claim of a winning tile. In other words, the current state of the hand does not produce yaku while tenpai. It is also called sakizuke 「先付け」.
The hand's waiting patterns includes tiles which do produce valid hands. Normally, this situation involves open hands. These typically involve yakuhai; and naturally, other yaku may be involved as well. The term may apply to closed hands, until it wins on a tile draw for mentsumo. The use of atozuke is subject to a variable rule, which may or may not allow its use. That decision falls on a league, organization, or house rule.
Rule variations allow organizations and/or tournament hosts to use atozuke. More commonly, atozuke is allowed.
Atozuke may be employed in a number of hands while in tenpai.
For all these examples, the yaku of haitei, houtei, or even rinshan, would render atozuke as moot, as yaku may apply to any needed winning tile. So, if the hand draws the lesser desired tile, then the hand may not qualify for a win. The same case applies for discards. If a win is declared on the improper tile, then the penalty of chombo is invoked for winning a hand without a yaku.
This time, the same tiles from the above hand has an open call. At it stands, it needs the haku in order to win.
This hand has an apparent yaku of sanshoku doukou. However, the latter wait of 3-sou would create a sequence of 1-2-3 sou, as it triggers the effect applied by the lesser valued tile. Suddenly, the required triplet of the three 1-sou disqualifies the apparent yaku.
Sanshoku is hinted at, however, the extended nobetan wait of 1-4-7s in the hand can ignore sanshoku on a 1s wait.
In these examples, atozuke is not used. In these cases, the hands may win on any of the waiting tiles without the enforcement of the chombo penalty. They each have valid yaku already embedded into the hand, regardless of their winning tiles.
Sanshoku is already embedded in the hand.
This hand employs honitsu.
Risk of furiten
Particularly, open yakuless hands run the risk of furiten. That is especially true if the above example draws a 9-pin during the course of the hand, when additional tile draws remain in the wall. In this case, a player cannot declare a win and must discard any tile in the hand. Upon doing so, the player becomes furiten and must work around it, by changing its hand composition with the remaining tile draws or other player discards. Otherwise, the player needs to retain the hand at tenpai waiting for the appropriate winning tile or to let the hand end with ryuukyoku.